Finite Group Databasebeta

← #25063069

Subgroups — #25063069

Order 11008.

1222 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063371C211yesmaximal, characteristic
2#19143714C211yesmaximal, characteristic, complemented
3#19143559C211yesmaximal, characteristic, complemented
4#19133037C211yesmaximal, characteristic, complemented
5#19133036C211yesmaximal, characteristic, complemented
6#19133034C211yesmaximal, characteristic, complemented
7#19133033C211yesmaximal, characteristic, complemented
8#19133028C211yesmaximal, characteristic, complemented
9#19133021C211yesmaximal, characteristic, complemented
10#19133018C211yesmaximal, characteristic, complemented
11#19132984C211yesmaximal, characteristic, complemented
12#19132981C211yesmaximal, characteristic, complemented
13#19132976C211yesmaximal, characteristic, complemented
14D4⋊C8×D43C211yesmaximal, characteristic, complemented
15C43×#1488C211yesmaximal, characteristic, complemented
16C2×#13063371C411yescharacteristic
17#14583382C411yescharacteristic
18#14583381C411yescharacteristic
19#14583381C411yescharacteristic
20#14583379—21no—
21#14583379C411yescharacteristic
22#14583373—21no—
23#14583373C411yescharacteristic
24#14583371—21no—
25#14583371—21no—
26#14583371C411yescharacteristic
27#14583371C411yescharacteristic
28C4×#10621902C2211yescharacteristic
29C4×#10621902C2211yescharacteristic
30C4×#10621898—21no—
31C4×#10621898C2211yescharacteristic
32C2×C4×D172—21no—
33C2×C4×D172C2211yescharacteristic
34C4×D4×D43—21no—
35C4×D4×D43—21no—
36C4×D4×D43C2211yescharacteristic
37C4×D4×D43C2211yescharacteristic
38#14583028—21no—
39#14583027—21no—
40#14582974—21no—
41#14582974—21no—
42#14582973—21no—
43#14582973—21no—
44#14582972—21no—
45#14582969—21no—
46#14582955C2211yescharacteristic, complemented
47#14582951C2211yescharacteristic, complemented
48#14582950C2211yescharacteristic, complemented
49#14582950C2211yescharacteristic, complemented
50#14582923C2211yescharacteristic, complemented
51#14582921C2211yescharacteristic, complemented
52C4⋊C8×D43C2211yescharacteristic, complemented
53C4×#10621877C2211yescharacteristic, complemented
54C4×#10621872C2211yescharacteristic, complemented
55C4×C8×D43C2211yescharacteristic, complemented
56Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
57Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
58#14582628C2211yescharacteristic, complemented
59#14582628C2211yescharacteristic, complemented
60#14582628C2211yescharacteristic, complemented
61#14582628C2211yescharacteristic, complemented
62D4⋊(C43⋊C8)C2211yescharacteristic, complemented
63D4⋊(C43⋊C8)C2211yescharacteristic, complemented
64#14582626C2211yescharacteristic, complemented
65#14582626C2211yescharacteristic, complemented
66#14582626C2211yescharacteristic, complemented
67#14582626C2211yescharacteristic, complemented
68C4×#41×C43C2211yescharacteristic
69C43×#432C2211yescharacteristic, complemented
70C43×#431C2211yescharacteristic, complemented
71C43×Q8⋊C8C2211yescharacteristic, complemented
72C43×Q8⋊C8C2211yescharacteristic, complemented
73C43×D4⋊C8C2211yescharacteristic, complemented
74C43×D4⋊C8C2211yescharacteristic, complemented
75#13063371—24no—
76#13063371—24no—
77C2×#10621902C2×C411yescharacteristic
78C2×#10621902C2×C411yescharacteristic
79C2×#10621898—21no—
80C2×#10621898C2×C411yescharacteristic
81C22×D172—21no—
82C22×D172C2×C411yescharacteristic
83C2×D4×D43—21no—
84C2×D4×D43—21no—
85C2×D4×D43C2×C411yescharacteristic
86C2×D4×D43C2×C411yescharacteristic
87C22×C4×D43—21no—
88C22×C4×D43—21no—
89C22×C4×D43—21no—
90C2×#10621877—21no—
91C2×#10621877—21no—
92C2×#10621872—21no—
93C2×#10621872—21no—
94C2×C8×D43—21no—
95C2×C8×D43—21no—
96Q8×Dic43C2×C411yescharacteristic
97Q8×Dic43C2×C411yescharacteristic
98C4×Dic86—21no—
99C4×Dic86D411yescharacteristic
100C4×Dic86D411yescharacteristic
101C4×D172—21no—
102C4×D172—21no—
103C4×D172—21no—
104C4×D172—21no—
105C4×D172—21no—
106C4×D172—21no—
107C4×D172—21no—
108C4×D172—21no—
109C4×D172—21no—
110C4×D172C2×C411yescharacteristic
111C4×D172C2×C411yescharacteristic
112C4×D172D411yescharacteristic
113C4×D172D411yescharacteristic
114C4×D172C2311yescharacteristic
115C4×D172C2311yescharacteristic
116D4×Dic43—21no—
117D4×Dic43—21no—
118D4×Dic43C2×C411yescharacteristic
119D4×Dic43C2×C411yescharacteristic
120#13063287—21no—
121#13063287—21no—
122#13063287—21no—
123#13063287—21no—
124#13063287C2×C411yescharacteristic
125#13063287C2×C411yescharacteristic
126#13063287C2×C411yescharacteristic
127#13063287C2×C411yescharacteristic
128C4×C22⋊D43—21no—
129C4×C22⋊D43—21no—
130C4×C22⋊D43—21no—
131C4×C22⋊D43—21no—
132C4×C22⋊D43D411yescharacteristic
133C4×C22⋊D43D411yescharacteristic
134C4×C22⋊D43D411yescharacteristic
135C4×C22⋊D43D411yescharacteristic
136(C22⋊D43)⋊C4—21no—
137(C22⋊D43)⋊C4—21no—
138(C22⋊D43)⋊C4—21no—
139(C22⋊D43)⋊C4—21no—
140(C22⋊D43)⋊C4—21no—
141(C22⋊D43)⋊C4—21no—
142#13063284—21no—
143#13063284C2×C411yescharacteristic
144#13063283—21no—
145#13063283—21no—
146#13063283C2×C411yescharacteristic
147#13063283C2×C411yescharacteristic
148#13063282—21no—
149#13063282—21no—
150#13063282C2×C411yescharacteristic
151#13063282C2×C411yescharacteristic
152C2×C4⋊Dic43—21no—
153C2×C4⋊Dic43C2×C411yescharacteristic
154C4⋊C4×D43—21no—
155C4⋊C4×D43—21no—
156C4⋊C4×D43C2×C411yescharacteristic
157C4⋊C4×D43C2×C411yescharacteristic
158C2×(C2×D43)⋊C4—21no—
159C2×(C2×D43)⋊C4—21no—
160C2×(C2×D43)⋊C4—21no—
161C22⋊C4×D43—21no—
162C22⋊C4×D43—21no—
163C22⋊C4×D43—21no—
164C22⋊C4×D43—21no—
165C22⋊C4×D43—21no—
166C22⋊C4×D43—21no—
167C42×D43—21no—
168C42×D43—21no—
169C42×D43C2311yescharacteristic
170C42×D43C2311yescharacteristic
171C4⋊(C43⋊C8)—21no—
172C4⋊(C43⋊C8)C2311yescharacteristic
173C4⋊(C43⋊C8)C2311yescharacteristic
174Dic43⋊C8—21no—
175Dic43⋊C8—21no—
176Dic43⋊C8—21no—
177Dic43⋊C8—21no—
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181(C2×D43)⋊C8—21no—
182#13063236—21no—
183#13063235—21no—
184#13063235—21no—
185C4×C43⋊C8C2311yescharacteristic
186C4×C43⋊C8C2311yescharacteristic
187C8×Dic43—21no—
188C8×Dic43—21no—
189C2×#41×C43C2×C411yescharacteristic
190C4×Q8×C43C2×C411yescharacteristic
191C4×Q8×C43C2311yescharacteristic
192C4×D4×C43—21no—
193C4×D4×C43—21no—
194C4×D4×C43C2×C411yescharacteristic
195C4×D4×C43C2311yescharacteristic
196#117×C43—21no—
197#117×C43C2×C411yescharacteristic
198C2×C42×C43—21no—
199C2×C42×C43C2311yescharacteristic
200C4⋊C8×C43—21no—
201C4⋊C8×C43C2311yescharacteristic
202C4⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43—21no—
204C22⋊C8×C43—21no—
205#97×C43—21no—
206C4×C8×C43C2311yescharacteristic
207C4×C8×C43C2311yescharacteristic
208C23×D43—21no—
209C23×D43—21no—
210C23×D43—21no—
211#41×C43—22no—
212#41×C43—22no—
213C2×Q8×C43C22×C411yescharacteristic
214C2×D4×C43—21no—
215C2×D4×C43C22×C411yescharacteristic
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43C22×C411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C2×C22⋊D43—21no—
223C2×C22⋊D43—21no—
224C2×C22⋊D43C22⋊C411yescharacteristic
225C2×C22⋊D43C22⋊C411yescharacteristic
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43—21no—
229#10621902—22no—
230#10621902—22no—
231#10621902—22no—
232#10621902M1614yescomplemented
233D4×D43—28no—
234D4×D43—28no—
235D4×D43—22no—
236D4×D43—22no—
237D4×D43—22no—
238D4×D43M1614yescomplemented
239#10621898—28no—
240#10621898—22no—
241#10621898—22no—
242C2×D172—28no—
243C2×D172—21no—
244C2×D172—22no—
245C2×D172—22no—
246C2×D172—21no—
247C2×D172—21no—
248C2×D172C22⋊C411yescharacteristic
249C2×D172C22×C411yescharacteristic
250C2×D172C22×C411yescharacteristic
251C2×C4×D43—21no—
252C2×C4×D43—21no—
253C2×C4×D43—21no—
254C2×C4×D43—21no—
255C2×C4×D43—21no—
256C2×C4×D43—21no—
257C2×C4×D43—21no—
258C2×C4×D43—21no—
259C2×C4×D43—21no—
260C2×C4×D43—21no—
261C2×C4×D43—21no—
262C2×C4×D43—21no—
263C2×C4×D43—81no—
264C2×C4×D43—81no—
265C2×C4×D43—81no—
266C2×C4×D43—81no—
267C2×C4×D43—81no—
268C2×C4×D43—81no—
269C2×C4×D43C22×C411yescharacteristic
270C2×C4×D43C22×C411yescharacteristic
271C2×C4×D43C2×D411yescharacteristic
272C2×C4×D43C2×D411yescharacteristic
273C2×C4×D43C2×D411yescharacteristic
274C2×C4×D43C2×D411yescharacteristic
275C2×Dic86C22⋊C411yescharacteristic
276C2×C8×C43—21no—
277C2×C8×C43—21no—
278C2×C8×C43—21no—
279C2×C8×C43—21no—
280C4⋊C4×C43—21no—
281C4⋊C4×C43—21no—
282C4⋊C4×C43C22×C411yescharacteristic
283C4⋊C4×C43C22×C411yescharacteristic
284C22⋊C4×C43—21no—
285C22⋊C4×C43—21no—
286C22⋊C4×C43—21no—
287C42×C43—21no—
288C42×C43—21no—
289C42×C43—21no—
290C42×C43C22×C411yescharacteristic
291C42×C43C2×D411yescharacteristic
292C42×C43C2×D411yescharacteristic
293C42×C43C2411yescharacteristic
294C22⋊Dic43—21no—
295C22⋊Dic43—21no—
296C22⋊Dic43C22⋊C411yescharacteristic
297C22⋊Dic43C22⋊C411yescharacteristic
298(C2×D43)⋊C4—21no—
299(C2×D43)⋊C4—21no—
300(C2×D43)⋊C4—21no—
301(C2×D43)⋊C4—21no—
302(C2×D43)⋊C4—21no—
303(C2×D43)⋊C4—21no—
304(C2×D43)⋊C4—21no—
305(C2×D43)⋊C4—21no—
306(C2×D43)⋊C4—21no—
307(C2×D43)⋊C4—21no—
308(C2×D43)⋊C4C22⋊C411yescharacteristic
309(C2×D43)⋊C4C22⋊C411yescharacteristic
310(C2×D43)⋊C4C22⋊C411yescharacteristic
311(C2×D43)⋊C4C22⋊C411yescharacteristic
312C4⋊Dic43—21no—
313C4⋊Dic43—21no—
314C4⋊Dic43—21no—
315C4⋊Dic43C22⋊C411yescharacteristic
316C4⋊Dic43C22⋊C411yescharacteristic
317C4⋊Dic43C22×C411yescharacteristic
318C4⋊Dic43C22×C411yescharacteristic
319Dic43⋊C4—21no—
320Dic43⋊C4—21no—
321Dic43⋊C4C22⋊C411yescharacteristic
322Dic43⋊C4C22⋊C411yescharacteristic
323Dic43⋊C4C22⋊C411yescharacteristic
324Dic43⋊C4C22⋊C411yescharacteristic
325C4×Dic43—21no—
326C4×Dic43—21no—
327C4×Dic43—21no—
328C4×Dic43—21no—
329C4×Dic43C22×C411yescharacteristic
330C4×Dic43C22×C411yescharacteristic
331C4×Dic43C2×D411yescharacteristic
332C4×Dic43C2×D411yescharacteristic
333C4×Dic43C2×D411yescharacteristic
334C4×Dic43C2×D411yescharacteristic
335#10621877—42no—
336#10621877—81no—
337C2×C43⋊C8—21no—
338C2×C43⋊C8—21no—
339C2×C43⋊C8—21no—
340C2×C43⋊C8—21no—
341#10621872—42no—
342#10621872—81no—
343C8×D43—42no—
344C8×D43—81no—
345C23×C43—21no—
346C23×C43C2×C22⋊C411yescharacteristic
347C22×D43—21no—
348C22×D43—21no—
349C22×D43—24no—
350C22×D43—24no—
351C22×D43—24no—
352C22×D43—81no—
353C22×D43—81no—
354C22×D43—81no—
355C22×D43—81no—
356C22×D43—81no—
357C22×D43—81no—
358C22×D43C2×C22⋊C411yescharacteristic
359C22×D43C2×C22⋊C411yescharacteristic
360Q8×C43—21no—
361Q8×C43C2×M1612yes—
362D4×C43—24no—
363D4×C43—21no—
364D4×C43C2×M1612yes—
365C2×C4×C43—24no—
366C2×C4×C43—21no—
367C2×C4×C43—21no—
368C2×C4×C43—21no—
369C2×C4×C43—21no—
370C2×C4×C43—21no—
371C2×C4×C43—21no—
372C2×C4×C43—21no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—81no—
377C2×C4×C43C2×C22⋊C411yescharacteristic
378C2×C4×C43C2×C22⋊C411yescharacteristic
379C2×C4×C43C2×C22⋊C411yescharacteristic
380C2×C4×C43C23×C411yescharacteristic
381C2×C4×C43C22×D411yescharacteristic
382C2×C4×C43C22×D411yescharacteristic
383C22⋊D43—24no—
384C22⋊D43—22no—
385C22⋊D43—22no—
386C22⋊D43—24no—
387C2×Dic43—21no—
388C2×Dic43—21no—
389C2×Dic43—81no—
390C2×Dic43—81no—
391C2×Dic43—81no—
392C2×Dic43C2×C22⋊C411yescharacteristic
393C2×Dic43C2×C22⋊C411yescharacteristic
394C2×Dic43C2×C22⋊C411yescharacteristic
395C2×Dic43C2×C22⋊C411yescharacteristic
396C2×Dic43C2×C22⋊C411yescharacteristic
397C2×Dic43C2×C22⋊C411yescharacteristic
398D172—24no—
399D172—24no—
400D172—22no—
401D172—24no—
402D172—21no—
403D172—21no—
404D172C2×M1612yes—
405D172C2×M1612yes—
406C4×D43—24no—
407C4×D43—21no—
408C4×D43—21no—
409C4×D43—21no—
410C4×D43—21no—
411C4×D43—21no—
412C4×D43—21no—
413C4×D43—24no—
414C4×D43—41no—
415C4×D43—41no—
416C4×D43—41no—
417C4×D43—41no—
418C4×D43—41no—
419C4×D43—41no—
420C4×D43—81no—
421C4×D43—81no—
422C4×D43—81no—
423C4×D43—81no—
424C4×D43—81no—
425C4×D43—81no—
426C4×D43—81no—
427C4×D43—81no—
428C4×D43C2×M1612yes—
429C4×D43C2×M1612yes—
430Dic86—22no—
431C8×C43—41no—
432C8×C43—41no—
433C8×C43—41no—
434C8×C43—41no—
435C43⋊C8—22no—
436C43⋊C8—41no—
437C43⋊C8—41no—
438C43⋊C8—41no—
439#17453—431nomaximal, Sylow
440C22×C43—22no—
441C22×C43—21no—
442C22×C43—21no—
443C22×C43—21no—
444C22×C43—41no—
445C22×C43—41no—
446C22×C43C22×C22⋊C411yescharacteristic
447C2×D43—21no—
448C2×D43—21no—
449C2×D43—22no—
450C2×D43—22no—
451C2×D43—21no—
452C2×D43—21no—
453C2×D43—21no—
454C2×D43—41no—
455C2×D43—41no—
456C2×D43—41no—
457C2×D43—41no—
458C2×D43—84no—
459C2×D43—84no—
460C2×D43—84no—
461C2×D43#40712yes—
462C4×C43—21no—
463C4×C43—22no—
464C4×C43—21no—
465C4×C43—21no—
466C4×C43—21no—
467C4×C43—41no—
468C4×C43—41no—
469C4×C43C22×M1611yescharacteristic
470C4×C43C22×M1611yescharacteristic
471C4×C43#57611yescharacteristic
472C4×C43#57711yescharacteristic
473Dic43—21no—
474Dic43—21no—
475Dic43—21no—
476Dic43—21no—
477Dic43—21no—
478Dic43—41no—
479Dic43—41no—
480Dic43#40712yes—
481C4×H(5,𝔽2)—431no—
482#2989—431no—
483#2965—431no—
484#1490—431no—
485#1490—431no—
486#1489—431no—
487#1489—431no—
488#1488—431no—
489#1488D4311yescharacteristic, complemented
490#1486—431no—
491#1486—431no—
492#1478—431no—
493#1477—431no—
494#1476—431no—
495C2×D4⋊C8—431no—
496C2×C43—41no—
497C2×C43—42no—
498C2×C43C2×#40711yescharacteristic
499C2×C43#289711yescharacteristic
500C2×C43#290111yescharacteristic
501D43—22no—
502D43—41no—
503D43—42no—
504D43—42no—
505C2×H(5,𝔽2)—431no—
506#520—431no—
507#520—431no—
508#520—431no—
509#520—431no—
510#520—861no—
511#518—431no—
512#518—431no—
513#518—431no—
514#518—861no—
515#518—861no—
516#518—861no—
517C4×#41—431no—
518C4×#41—431no—
519C4×#41—431no—
520C4×#41—861no—
521C4×#41C2×D4311yescharacteristic
522C2×C4×D4—431no—
523C2×C4×D4—431no—
524C2×C4×D4—431no—
525C2×C4×D4—861no—
526C2×C4×D4—861no—
527C2×C4×D4—861no—
528#446—861no—
529#446—861no—
530#436—861no—
531#436—861no—
532#435—861no—
533#435—861no—
534#435—861no—
535#435—861no—
536#432—431no—
537#432C2×D4311yescharacteristic, complemented
538#431—431no—
539#431—431no—
540#431—431no—
541#431C2×D4311yescharacteristic, complemented
542#423—431no—
543#423—431no—
544C2×C4⋊C8—431no—
545C4×M16—431no—
546C4×M16—431no—
547C2×C4×C8—431no—
548Q8⋊C8—431no—
549Q8⋊C8—431no—
550Q8⋊C8C2×D4311yescharacteristic, complemented
551Q8⋊C8C2×D4311yescharacteristic, complemented
552D4⋊C8—431no—
553D4⋊C8—431no—
554D4⋊C8—431no—
555D4⋊C8—431no—
556D4⋊C8—431no—
557D4⋊C8—431no—
558D4⋊C8—431no—
559D4⋊C8—431no—
560D4⋊C8—431no—
561D4⋊C8—431no—
562D4⋊C8C2×D4311yescharacteristic, complemented
563D4⋊C8C2×D4311yescharacteristic, complemented
564C43#1745311yescharacteristic, complemented, Sylow
565H(5,𝔽2)—864no—
566H(5,𝔽2)—864no—
567C2×#41—431no—
568C2×#41—431no—
569C2×#41—431no—
570C2×#41—861no—
571C2×#41C4×D4311yescharacteristic
572C22×D4—431no—
573C22×D4—431no—
574C22×D4—431no—
575C22×D4—861no—
576C22×D4—861no—
577C22×D4—861no—
578C23×C4—861no—
579C23×C4—861no—
580C23×C4—861no—
581C2×M16—861no—
582C2×M16—861no—
583C2×M16—861no—
584C2×M16—861no—
585C22×C8—861no—
586C22×C8—861no—
587C4×Q8—431no—
588C4×Q8—431no—
589C4×Q8—431no—
590C4×Q8—431no—
591C4×Q8—861no—
592C4×Q8C4×D4311yescharacteristic
593C4×Q8C22×D4311yescharacteristic
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—431no—
597C4×D4—431no—
598C4×D4—431no—
599C4×D4—431no—
600C4×D4—431no—
601C4×D4—431no—
602C4×D4—431no—
603C4×D4—431no—
604C4×D4—431no—
605C4×D4—431no—
606C4×D4—431no—
607C4×D4—431no—
608C4×D4—431no—
609C4×D4—431no—
610C4×D4—431no—
611C4×D4—431no—
612C4×D4—861no—
613C4×D4—861no—
614C4×D4—861no—
615C4×D4—861no—
616C4×D4—861no—
617C4×D4—861no—
618C4×D4—861no—
619C4×D4—861no—
620C4×D4—861no—
621C4×D4—861no—
622C4×D4—861no—
623C4×D4—861no—
624C4×D4—861no—
625C4×D4—861no—
626C4×D4—861no—
627C4×D4—861no—
628C4×D4—861no—
629C4×D4—861no—
630C4×D4—861no—
631C4×D4—861no—
632C4×D4—861no—
633C4×D4—861no—
634C4×D4—861no—
635C4×D4—861no—
636C4×D4—861no—
637C4×D4C4×D4311yescharacteristic
638C4×D4C22×D4311yescharacteristic
639#117—21no—
640#117—431no—
641#117—431no—
642#117—431no—
643#117—431no—
644#117—431no—
645#117—861no—
646#117—861no—
647#117—861no—
648#117—861no—
649#117—861no—
650#117C4×D4311yescharacteristic
651C2×C4⋊C4—431no—
652C2×C4⋊C4—431no—
653C2×C4⋊C4—431no—
654C2×C4⋊C4—861no—
655C2×C4⋊C4—861no—
656C2×C4⋊C4—861no—
657C2×C22⋊C4—861no—
658C2×C22⋊C4—861no—
659C2×C22⋊C4—861no—
660C2×C22⋊C4—861no—
661C2×C22⋊C4—861no—
662C2×C22⋊C4—861no—
663C2×C22⋊C4—861no—
664C2×C22⋊C4—861no—
665C2×C22⋊C4—861no—
666C2×C42—21no—
667C2×C42—431no—
668C2×C42—431no—
669C2×C42—861no—
670C2×C42—861no—
671C2×C42C22×D4311yescharacteristic
672C4⋊C8—21no—
673C4⋊C8—431no—
674C4⋊C8—431no—
675C4⋊C8—861no—
676C4⋊C8—861no—
677C4⋊C8—861no—
678C4⋊C8—861no—
679C4⋊C8—861no—
680C4⋊C8C22×D4311yescharacteristic
681C4⋊C8C22×D4311yescharacteristic
682C22⋊C8—21no—
683C22⋊C8—21no—
684C22⋊C8—861no—
685C22⋊C8—861no—
686C22⋊C8—861no—
687C22⋊C8—861no—
688#97—21no—
689#97—861no—
690#97—861no—
691#97—861no—
692C4×C8—431no—
693C4×C8—431no—
694C4×C8—861no—
695C4×C8—861no—
696C4×C8C22×D4311yescharacteristic
697C4×C8C22×D4311yescharacteristic
698C24—861no—
699C24—861no—
700C24—861no—
701#41—22no—
702#41—22no—
703#41—434no—
704#41—862no—
705#41—862no—
706#41—868no—
707#41—862no—
708#41—862no—
709#41—862no—
710C2×Q8—431no—
711C2×Q8C2×C4×D4311yescharacteristic
712C2×D4—21no—
713C2×D4—434no—
714C2×D4—431no—
715C2×D4—431no—
716C2×D4—431no—
717C2×D4—431no—
718C2×D4—431no—
719C2×D4—862no—
720C2×D4—862no—
721C2×D4—861no—
722C2×D4—861no—
723C2×D4—868no—
724C2×D4—862no—
725C2×D4—861no—
726C2×D4—861no—
727C2×D4—862no—
728C2×D4—868no—
729C2×D4—868no—
730C2×D4—862no—
731C2×D4—861no—
732C2×D4C2×C4×D4311yescharacteristic
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—431no—
737C22×C4—431no—
738C22×C4—431no—
739C22×C4—431no—
740C22×C4—431no—
741C22×C4—431no—
742C22×C4—861no—
743C22×C4—861no—
744C22×C4—861no—
745C22×C4—861no—
746C22×C4—861no—
747C22×C4—861no—
748C22×C4—861no—
749C22×C4—861no—
750C22×C4—861no—
751C22×C4—861no—
752C22×C4—861no—
753C22×C4—861no—
754C22×C4—861no—
755C22×C4—861no—
756C22×C4—861no—
757C22×C4—3441no—
758C22×C4—3441no—
759C22×C4—3441no—
760C22×C4—3441no—
761C22×C4—3441no—
762C22×C4—3441no—
763C22×C4C2×C4×D4311yescharacteristic
764C22×C4D4×D4311yescharacteristic
765C22×C4D4×D4311yescharacteristic
766M16—3441no—
767M16—3441no—
768M16—1722no—
769M16—1722no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—861no—
775C2×C8—861no—
776C2×C8—861no—
777C2×C8—861no—
778C2×C8—3441no—
779C2×C8—1722no—
780C4⋊C4—21no—
781C4⋊C4—21no—
782C4⋊C4—431no—
783C4⋊C4—431no—
784C4⋊C4—431no—
785C4⋊C4—431no—
786C4⋊C4—431no—
787C4⋊C4—431no—
788C4⋊C4—431no—
789C4⋊C4—431no—
790C4⋊C4—861no—
791C4⋊C4—861no—
792C4⋊C4—861no—
793C4⋊C4—861no—
794C4⋊C4—861no—
795C4⋊C4C2×C4×D4311yescharacteristic
796C4⋊C4C2×C4×D4311yescharacteristic
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—431no—
801C22⋊C4—431no—
802C22⋊C4—431no—
803C22⋊C4—431no—
804C22⋊C4—431no—
805C22⋊C4—431no—
806C22⋊C4—861no—
807C22⋊C4—861no—
808C22⋊C4—861no—
809C22⋊C4—861no—
810C22⋊C4—861no—
811C22⋊C4—861no—
812C22⋊C4—861no—
813C22⋊C4—861no—
814C22⋊C4—861no—
815C22⋊C4—861no—
816C22⋊C4—861no—
817C22⋊C4—861no—
818C42—21no—
819C42—21no—
820C42—21no—
821C42—431no—
822C42—431no—
823C42—431no—
824C42—431no—
825C42—431no—
826C42—431no—
827C42—861no—
828C42—861no—
829C42—861no—
830C42—861no—
831C42C2×C4×D4311yescharacteristic
832C42D4×D4311yescharacteristic
833C42D4×D4311yescharacteristic
834C42C23×D4311yescharacteristic
835C23—21no—
836C23—431no—
837C23—431no—
838C23—864no—
839C23—864no—
840C23—864no—
841C23—861no—
842C23—861no—
843C23—3441no—
844C23—3441no—
845C23—3441no—
846C23—3441no—
847C23—3441no—
848C23—3441no—
849C23C22⋊C4×D4311yescharacteristic
850Q8—21no—
851Q8—862no—
852Q8M16×D4312yes—
853D4—24no—
854D4—21no—
855D4—432no—
856D4—432no—
857D4—862no—
858D4—864no—
859D4—864no—
860D4—864no—
861D4—862no—
862D4—864no—
863D4—862no—
864D4—864no—
865D4—861no—
866D4—861no—
867D4M16×D4312yes—
868C2×C4—24no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—81no—
880C2×C4—431no—
881C2×C4—432no—
882C2×C4—432no—
883C2×C4—431no—
884C2×C4—431no—
885C2×C4—431no—
886C2×C4—431no—
887C2×C4—431no—
888C2×C4—864no—
889C2×C4—864no—
890C2×C4—861no—
891C2×C4—861no—
892C2×C4—861no—
893C2×C4—861no—
894C2×C4—861no—
895C2×C4—861no—
896C2×C4—861no—
897C2×C4—861no—
898C2×C4—3441no—
899C2×C4—3441no—
900C2×C4—3441no—
901C2×C4—3441no—
902C2×C4—3441no—
903C2×C4—3441no—
904C2×C4—3441no—
905C2×C4—3441no—
906C2×C4—3441no—
907C2×C4—3441no—
908C2×C4—3441no—
909C2×C4—1721no—
910C2×C4—1721no—
911C2×C4—1721no—
912C2×C4—1721no—
913C2×C4—1721no—
914C2×C4—1721no—
915C2×C4C22⋊C4×D4311yescharacteristic
916C2×C4C22⋊C4×D4311yescharacteristic
917C2×C4C22⋊C4×D4311yescharacteristic
918C2×C4C22×C4×D4311yescharacteristic
919C2×C4C2×D4×D4311yescharacteristic
920C2×C4C2×D4×D4311yescharacteristic
921C8—41no—
922C8—41no—
923C8—41no—
924C8—41no—
925C8—862no—
926C8—1721no—
927C8—1721no—
928C8—1721no—
929C22—21no—
930C22—22no—
931C22—21no—
932C22—21no—
933C22—41no—
934C22—41no—
935C22—432no—
936C22—861no—
937C22—861no—
938C22—862no—
939C22—862no—
940C22—861no—
941C22—861no—
942C22—861no—
943C22—3444no—
944C22—3444no—
945C22—3444no—
946C22—1721no—
947C22—1721no—
948C22—1721no—
949C22—1721no—
950C22C2×C22⋊C4×D4311yescharacteristic
951C4—21no—
952C4—22no—
953C4—21no—
954C4—21no—
955C4—21no—
956C4—41no—
957C4—41no—
958C4—432no—
959C4—861no—
960C4—861no—
961C4—861no—
962C4—861no—
963C4—861no—
964C4—1721no—
965C4—1721no—
966C4C2×M16×D4311yescharacteristic
967C4C2×M16×D4311yescharacteristic
968C4#1458370111yescharacteristic
969C4#1458370611yescharacteristic
970C2—41no—
971C2—42no—
972C2—862no—
973C2—1721no—
974C2—1722no—
975C2—1722no—
976C2#407×D4311yescharacteristic
977C2#1914311711yescharacteristic
978C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1488C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063371C4
cosocleC42×C43C24
hypercenter#1488D43
hypocenterC43#17453
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #19143714C2semidirect
3. #19143559C2semidirect
4. #19133037C2semidirect
5. #19133036C2semidirect
6. #19133034C2semidirect
7. #19133033C2semidirect
8. #19133028C2semidirect
9. #19133021C2semidirect
10. #19133018C2semidirect
11. #19132984C2semidirect
12. #19132981C2semidirect
13. #19132976C2semidirect
14. D4⋊C8×D43C2semidirect
15. C43×#1488C2semidirect
46. #14582955C22semidirect
47. #14582951C22semidirect
48. #14582950C22semidirect
49. #14582950C22semidirect
50. #14582923C22semidirect
51. #14582921C22semidirect
52. C4⋊C8×D43C22semidirect
53. C4×#10621877C22semidirect
54. C4×#10621872C22semidirect
55. C4×C8×D43C22semidirect
56. Q8⋊(C43⋊C8)C22semidirect
57. Q8⋊(C43⋊C8)C22semidirect
58. #14582628C22semidirect
59. #14582628C22semidirect
60. #14582628C22semidirect
61. #14582628C22semidirect
62. D4⋊(C43⋊C8)C22semidirect
63. D4⋊(C43⋊C8)C22semidirect
64. #14582626C22semidirect
65. #14582626C22semidirect
66. #14582626C22semidirect
67. #14582626C22semidirect
69. C43×#432C22semidirect
70. C43×#431C22semidirect
71. C43×Q8⋊C8C22semidirect
72. C43×Q8⋊C8C22semidirect
73. C43×D4⋊C8C22semidirect
74. C43×D4⋊C8C22semidirect
232. #10621902M16semidirect
238. D4×D43M16semidirect
489. #1488D43semidirect
537. #432C2×D43semidirect
541. #431C2×D43semidirect
550. Q8⋊C8C2×D43semidirect
551. Q8⋊C8C2×D43semidirect
562. D4⋊C8C2×D43semidirect
563. D4⋊C8C2×D43semidirect
564. C43#17453semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C4×#130633712
#191437142
#191435592
#191330372
#191330362
#191330342
#191330332
#191330282
#191330212
#191330182
#191329842
#191329812
#191329762
D4⋊C8×D432
C43×#14882
#1745343